J. J. Ramos

Dipole equilibrium and stability

A plasma confined in a dipole field exhibits unique equilibrium and stability properties. In particular, equilibria exist at all beta values and these equilibria are found to be stable to ballooning modes when they are interchange stable. When a kinetic treatment is performed at low beta, a drift temperature gradient mode is also found which couples to the MHD mode in the vicinity of marginal interchange stability.

Fluid Formalism for Collisionless Magnetized Plasmas

A comprehensive analysis of the finite-Larmor-radius (FLR) fluid moment equations for collisionless magnetized plasmas is presented. It is based on perturbative but otherwise general solutions for the second and third rank fluid moments (the stress and stress flux tensors), with closure conditions still to be specified on the fourth rank moment. The single expansion parameter is the ratio between the largest among the gyroradii and any other characteristic length, which is assumed to be small but finite in a magnetized medium. This formalism allows a complete account of the gyroviscous stress, the pressure anisotropy, and the anisotropic heat fluxes, and is valid for arbitrary magnetic geometry, arbitrary plasma pressure, and fully electromagnetic nonlinear dynamics. As the result, very general yet notably compact perturbative systems of FLR collisionless fluid equations, applicable to either fast (sonic or Alfvenic) or slow (diamagnetic) motions, are obtained.

General expression of the gyroviscous force

Assuming only small gyromotion periods and Larmor radii compared to any other time and length scales, and retaining the lowest significant order in δ=ρi∕L⪡1, the general expression of the ion gyroviscous stress tensor is presented. This expression covers both the “fast dynamics” (or “magnetohydrodynamic”) ordering, where the time derivative and ion gyroviscous stress are first order in δ relative to the ion gyrofrequency and scalar pressure, respectively, and the “slow dynamics” (or “drift”) ordering, where the time derivative and ion gyroviscous stress are, respectively, second order in δ. This general stress tensor applies to arbitrary collisionality and does not require the distribution function to be close to a Maxwellian. Its exact divergence (gyroviscous force) is written in a closed vector form, allowing for arbitrary magnetic geometry, parallel gradients, and flow velocities. Considering, in particular, the contribution from the velocity gradient (rate of strain) term, the final form of the moment...

Variational principle for low‐frequency stability of collisionless plasmas

An analysis of the stability of an arbitrary β collisionless plasma to modes with wavelengths greater than the ion gyroradius is presented. The stability of such a plasma to perturbations that grow on the hydrodynamic time scale is determined by the Kruskal–Oberman energy principle. However, a configuration which is predicted to be stable on the basis of this kinetic energy principle may still be unstable to modes that grow with a frequency comparable to the diamagnetic or curvature drift frequency. A new variational principle that gives sufficient conditions for instability of these low‐ frequency modes is derived. The new principle indicates that two types of instabilities are possible; the first corresponds to the low‐frequency electrostatic, trapped particles mode, and the second is the low‐frequency limit of magnetohydrodynamic (interchange and ballooning) modes. The kinetic modifications to the interchange (Mercier) criterion are evaluated and the effect of the kinetic terms on ballooning modes is e...

Ballooning stability of a point dipole equilibrium

The energy principle is employed to show that the equilibrium confined by the magnetic field of a point dipole is stable to ballooning modes.

Drift ballooning instabilities in tokamak edge plasmas

The linear stability of high-toroidal-number drift-ballooning modes in tokamaks is investigated with a model that includes resistive and viscous dissipation, and assumes the mode frequency to be comparable to both the sound and diamagnetic frequencies. The coupled effect of ion drift waves and electron drift-acoustic waves is shown to be important, resulting in destabilization over an intermediate range of toroidal mode numbers. The plasma parameters where the assumed orderings hold would be applicable to the edge conditions in present day tokamaks, so these instabilities might be related to the observed quasicoherent edge-localized fluctuations.

Effect of strong radial variation of the ion diamagnetic frequency on internal ballooning modes

The formalism for internal ballooning modes in a tokamak is extended to retain the strong radial variation of the ion diamagnetic drift frequency characteristic of edge plasmas in the pedestal region. The resulting finite Larmor radius (FLR) stabilization is modified and can be weaker than in the case of constant diamagnetic frequency.

Access to the second stability region in a high-shear, low-aspect-ratio tokamak

It is known that tokamaks display a second region of stability to ideal magnetohydrodynamic (MHD) internal modes. An important determining factor for MHD properties is the radial profile of toroidal current. Here it is shown that in a low‐aspect‐ratio tokamak with high on‐axis safety factor (q0≂2) and high shear, a path to high beta can be obtained that remains completely stable against ideal MHD modes. By maintaining high shear this scenario avoids fixed boundary instabilities for both high and low toroidal mode numbers for beta values well above the Troyon limit (stability was tested up to eβp=1.4, β=10.8%). For a close fitting wall (awall/aplasma≂1.2) this configuration is also stable to low toroidal mode number balloon‐kink modes.

Fluid theory of magnetized plasma dynamics at low collisionality

Finite Larmor radius (FLR) fluid equations for magnetized plasmas evolving on either sonic or diamagnetic drift time scales are derived consistent with a broad low-collisionality hypothesis. The fundamental expansion parameter is the ratio δ between the ion Larmor radius and the shortest macroscopic length scale (including fluctuation wavelengths in the absence of small scale turbulence). The low-collisionality regime of interest is specified by assuming that the other two basic small parameters—namely, the ratio between the electron and ion masses and the ratio between the ion collision and cyclotron frequencies—are comparable to or smaller than δ2. First significant order FLR equations for the stress tensors and the heat fluxes are given, including a detailed discussion of the collisional terms that need be retained under the assumed orderings and of the closure terms that need be determined kinetically. This analysis is valid for any magnetic geometry and for fully electromagnetic nonlinear dynamics wi...

Modelling of advanced tokamak scenarios with LHCD in Alcator C-Mod

A combined model for current profile control and MHD stability analysis has been used to identify stable operating modes near the ideal stability limit (?N 3) in the Alcator C-Mod tokamak. These discharges are characterized by relatively high fractions of bootstrap current (fBS = 0.70) and non-monotonic profiles of the safety factor with qmin > 2. In the absence of a conducting shell, stability was determined by the onset of the low (n = 1) external kink mode. In these studies, current profile control in the plasma periphery (r/a 0.5) was provided by 2.5-3.0?MW of LHCD power. Internal and edge transport barriers were introduced into the model calculations in the form of density transitions. Excellent wave accessibility and absorption were still found in the presence of an H-mode-like edge density barrier. However, the presence of these barriers resulted in about a 10% decrease in the stability limit, from ?N 3 to ?N 2.7.